Performance limitations of subband adaptive filters

In this paper, we evaluate the performance limitations of subband adaptive filters in terms of achievable final error terms. The limiting factors are the aliasing level in the subbands, which poses a distortion and thus presents a lower bound for the minimum mean squared error in each subband, and the distortion function of the overall filter bank, which in a system identification setup restricts the accuracy of the equivalent fullband model. Using a generalized DFT modulated filter bank for the subband decomposition, both errors can be stated in terms of the underlying prototype filter. If a source model for coloured input signals is available, it is also possible to calculate the power spectral densities in both subbands and reconstructed fullband. The predicted limits of error quantities compare favourably with simulations presented

Instabilities of Shercliffe and Stewartson layers in spherical Couette flow

We explore numerically the flow induced in a spherical shell by differentially rotating the inner and outer spheres. The fluid is also taken to be electrically conducting (in the low magnetic Reynolds number limit), and a magnetic field is imposed parallel to the axis of rotation. If the outer sphere is stationary, the magnetic field induces a Shercliffe layer on the tangent cylinder, the cylinder just touching the inner sphere and parallel to the field. If the magnetic field is absent, but a strong overall rotation is present, Coriolis effects induce a Stewartson layer on the tangent cylinder. The nonaxisymmetric instabilities of both types of layer separately have been studied before; here, we consider the two cases side by side, as well as the mixed case, and investigate how magnetic and rotational effects interact. We find that if the differential rotation and the overall rotation are in the same direction, the overall rotation may have a destabilizing influence, whereas if the differential rotation and the overall rotation are in the opposite direction, the overall rotation always has a stabilizing influence

Double Coronal Hard and Soft X-ray Source Observed by RHESSI: Evidence for Magnetic Reconnection and Particle Acceleration in Solar Flares

We present data analysis and interpretation of an M1.4-class flare observed with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) on April 30, 2002. This event, with its footpoints occulted by the solar limb, exhibits a rarely observed, but theoretically expected, double-source structure in the corona. The two coronal sources, observed over the 6-30 keV range, appear at different altitudes and show energy-dependent structures with the higher-energy emission being closer together. Spectral analysis implies that the emission at higher energies in the inner region between the two sources is mainly nonthermal, while the emission at lower energies in the outer region is primarily thermal. The two sources are both visible for about 12 minutes and have similar light curves and power-law spectra above about 20 keV. These observations suggest that the magnetic reconnection site lies between the two sources. Bi-directional outflows of the released energy in the form of turbulence and/or particles from the reconnection site can be the source of the observed radiation. The spatially resolved thermal emission below about 15 keV, on the other hand, indicates that the lower source has a larger emission measure but a lower temperature than the upper source. This is likely the result of the differences in the magnetic field and plasma density of the two sources.Comment: Accepted by ApJ (12/06/2007), scheduled for the 03/20/2008 Vol. 676 No. 1 Issue, 13 pages, 9 figure

Unified Picture for Magnetic Correlations in Iron-Based Superconductors

The varying metallic antiferromagnetic correlations observed in iron-based superconductors are unified in a model consisting of both itinerant electrons and localized spins. The decisive factor is found to be the sensitive competition between the superexchange antiferromagnetism and the orbital-degenerate double-exchange ferromagnetism. Our results reveal the crucial role of Hund's rule coupling for the strongly correlated nature of the system and suggest that the iron-based superconductors are closer kin to manganites than cuprates in terms of their diverse magnetism and incoherent normal-state electron transport. This unified picture would be instrumental for exploring other exotic properties and the mechanism of superconductivity in this new class of superconductors.Comment: Revised for publication. 3 figure

Poset-free Families and Lubell-boundedness

Given a finite poset $P$, we consider the largest size \lanp of a family \F of subsets of $[n]:=\{1,...,n\}$ that contains no subposet $P$. This continues the study of the asymptotic growth of \lanp; it has been conjectured that for all $P$, \pi(P):= \lim_{n\rightarrow\infty} \lanp/\nchn exists and equals a certain integer, $e(P)$. While this is known to be true for paths, and several more general families of posets, for the simple diamond poset \D_2, the existence of $\pi$ frustratingly remains open. Here we develop theory to show that $\pi(P)$ exists and equals the conjectured value $e(P)$ for many new posets $P$. We introduce a hierarchy of properties for posets, each of which implies $\pi=e$, and some implying more precise information about \lanp. The properties relate to the Lubell function of a family \F of subsets, which is the average number of times a random full chain meets \F. We present an array of examples and constructions that possess the properties

Nonlinear Dirac Equations

We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations

Maximizing sum rate and minimizing MSE on multiuser downlink: Optimality, fast algorithms and equivalence via max-min SIR

Maximizing the minimum weighted SIR, minimizing the weighted sum MSE and maximizing the weighted sum rate in a multiuser downlink system are three important performance objectives in joint transceiver and power optimization, where all the users have a total power constraint. We show that, through connections with the nonlinear Perron-Frobenius theory, jointly optimizing power and beamformers in the max-min weighted SIR problem can be solved optimally in a distributed fashion. Then, connecting these three performance objectives through the arithmetic-geometric mean inequality and nonnegative matrix theory, we solve the weighted sum MSE minimization and weighted sum rate maximization in the low to moderate interference regimes using fast algorithms

Combinatorial batch codes

In this paper, we study batch codes, which were introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [4]. A batch code specifies a method to distribute a database of [n] items among [m] devices (servers) in such a way that any [k] items can be retrieved by reading at most [t] items from each of the servers. It is of interest to devise batch codes that minimize the total storage, denoted by [N] , over all [m] servers. We restrict out attention to batch codes in which every server stores a subset of the items. This is purely a combinatorial problem, so we call this kind of batch code a ''combinatorial batch code''. We only study the special case [t=1] , where, for various parameter situations, we are able to present batch codes that are optimal with respect to the storage requirement, [N] . We also study uniform codes, where every item is stored in precisely [c] of the [m] servers (such a code is said to have rate [1/c] ). Interesting new results are presented in the cases [c = 2, k-2] and [k-1] . In addition, we obtain improved existence results for arbitrary fixed [c] using the probabilistic method